On the existence and stability of a two-dimensional relaxational torus (Q1905330)

The theory of relaxational oscillations for systems of ordinary differential equations with a small parameter at some derivatives has been currently developed sufficiently well to consider different applications. In particular, in the case of three-dimensional systems with one slow variable, the problem stated in the title of this paper was solved by the author and \textit{E. F. Mischenko} [Russ. Math. Surv. 44, No. 3, 204-205 (1989); translation from Usp. Mat. Nauk 44, No. 3 (267), 161- 162 (1989; Zbl 0704.34003)]. We now study this problem in the more complicated case of two slow variables. We also describe special mechanisms which lead to destruction of the relaxational torus.